What Lyn has said about the actual PSP itself is entirely correct.
On a sidenote, about the advertisement for it on ebay...
Go back to the items listing page and READ CAREFULLY what it says. Does it mention the PSP UMD holder problem? If it does, then unfortunately you've literally got what you paid for.
If, however, it does NOT mention that, then I would contact ebay about your problem and tell them that it was "not as described" and then go through it that way, you may, and I cant emphasize this enough, MAY, be eligible for some of your money back, but I doubt it.
I'd still check out what I've suggested though. Maybe the Seller does returns or something? No harm in asking I suppose.
Jay